Elementary Geometry from an Advanced Standpoint by Edwin E. Moise (PDF)

Description

Students can rely on Moise’s clear and thorough presentation of basic geometry theorems. The author assumes that students have no previous knowledge of the subject and presents the basics of geometry from the ground up. This comprehensive approach gives instructors flexibility in teaching. For example, an advanced class may progress rapidly through Chapters 1-7 and devote most of its time to the material presented in Chapters 8, 10, 14, 19, and 20. Similarly, a less advanced class may go carefully through Chapters 1-7, and omit some of the more difficult chapters, such as 20 and 24.

User’s Reviews

Editorial Reviews: From the Back Cover One of the purposes of this book is to reexamine geometry, to clean up behind introductory courses, furnishing valid definitions and valid proofs for concepts and theorems which were already known, at least in some sense and some form.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐Moise’s book has a long history. In the 1960’s, the same author wrote a simpler version of this book (with Downs) for use in high schools, a revolutionary deed since very precise mathematics is not usual in high school. One may be question if high school is the place to teach geometry in this way, but for the book written for undergrads this is unquestionable. I really do not know of any other book of its kind (there are advanced books of elementary geometry, but usually from the synthetic viewpoint which make them difficult to read at this point). In the same way that real analysis books (e.g., Apostol) gives for the student absolute rigour and precise proofs in the realm of real numbers and functions, Moise’s book do the same for elementary Euclidean geometry. And it does so with easy-to-follow arguments and a good historical discussion. Although focused on the easier analytical viewpoint, that starts with real numbers as given entities, it explains how to obtain the same results by the more beautiful and historical synthetic viewpoint. The book has irresistible taste, as other reviewers already pointed out. But it is much more than that. It is possible to be a graduated mathematician and still not be able to prove with rigour results from elementary geometry. This book gives you this power. Once read, you can complement it with other results from elementary books, that can be reworked with the formalism you get from Moise’s book. And you are much better prepared to understand more advanced books on the same subject, as the amazing Projective Geometry from Veblen and Young (probably one of the best books in Geometry ever written). So Elementary Geometry from an Advanced Viewpoint is really a book that gives immense power and helps you to understand the great human endeavour called Geometry. Very important work.

⭐We only covered the first 10 chapters or so, so I cannot offer a holistic review of the book. However, I can speak for the Euclidean material.This book offers a nice breakdown and organization of the basic geometric postulates and theorems. About 75% of the proofs were straightforward and appropriate. However, there were always a few that required another perspective to unravel. However, a good professor can shed the light needed for these mysteries.That is not why this text gets only 3 out of 5 stars. The exercise sets are not as thorough as one would hope. In fact, many of the exercises were fairly trivial. A reexamination of these exercises would take Moise’s expert breakdown of Euclidean geometry to the next level (in terms of advanced college mathematics textbooks). Again, a good professor can alleviate this problem, but why can’t the editors address this issue themselves?Overall, Moise’s treatment of Euclidean geometry is superb. I recommend this text wholeheartedly if you have an able professor that can elevate Moise’s work with meaningful exercise sets.

⭐I like the author’s writing style, which is mathematical yet humorous at times. I also like the emphasis on precision of mathematical language.

⭐This book has a few errors and is not very descriptive. However, it is a course requirement. So, I guess it has to be okay.

⭐This book was beneficial to me in the Euclidean Geometry course I took. I recommend using the newest edition out.

⭐Amazing book. By far the best geometry book written.

⭐Excellent

⭐As an exercise in considering how I might write my own Geometry book one day, a friend and colleague directed me at Moise’s title. I simply treated the book as both a trained mathematician and as an editor. Without a doubt, this book has been thoroughly built from the bottom up without flaw (save for, if I recall, 2 typos and 1 problem that in my opinion only deserved delay to a future section). Consider the hundreds of pages therein, this feat is monumental. While I would absolutely hate to learn geometry for a first time this way, an collegiate level student seeking to fully develop a sense of geometries (yes, plural) would be best served to take a few months as I did to challenge what you think you know by working (not skimming) your way through Moise’s material. It has earned its place amongst my favorite resource books for its thoroughness, its accuracy, and its thoughtfulness.

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